Nuclei

What you will understand

For NEET UG Physics students: count protons and neutrons, use a consistent mass convention for binding energy, separate remaining nuclei from decayed nuclei and calculate nuclear energy changes from total binding.

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Quick answer: conserve nucleon count and keep the mass reference consistent

Mass number A counts protons plus neutrons; atomic number Z counts protons. A bound nucleus has lower rest mass than its separated constituent nucleons, and its positive binding energy is the energy required to separate them. Use either nuclear masses with bare protons or a consistent atomic-mass formula with hydrogen atoms. Radioactive half-life concerns a remaining-parent population, while activity also includes the decay constant. Total binding and binding per nucleon answer different questions.

Helium binding: an atomic-mass convention cancels electron rest masses

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A, Z and radius describe different quantities

For a nuclide with A=56 and Z=26, proton count is 26 and neutron count is 30. Isotopes share Z but differ in neutron count; isobars share A, and isotones share neutron count. In the approximate radius law $R=R_0A^{1/3}$, increasing A by a factor of eight doubles R rather than multiplying it by eight. This scaling makes volume approximately proportional to nucleon count and density roughly independent of A in the simple model. A mass number is a count, not an exact atomic mass in u.

Half-life describes the remaining parent population

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Decay bookkeeping does not by itself prove that a decay occurs

An alpha emission changes A to A−4 and Z to Z−2. A beta-minus emission leaves A unchanged and raises Z by one, with an electron and an electron antineutrino in the final state. An ordinary gamma transition changes nuclear excitation without changing A or Z. For a hypothetical parent with A=240,Z=90, one alpha followed by one beta-minus gives A=236,Z=89. That is nucleon/charge bookkeeping; energetic feasibility and actual branching require more information. The emitted beta electron is not evidence of a pre-existing electron stored inside the nucleus.

One half-life does not schedule each nucleus

The exponential model assigns a decay probability per unit time to each remaining nucleus. It does not specify which nucleus will decay next or say every nucleus survives exactly one half-life. A nucleus that remains after one half-life is still described by the same constant decay probability in this model. The remaining population falls smoothly in the large-sample approximation, while individual events are random.

Common mistakes: total, per nucleon, remaining and activity are different

Do not mix atomic and nuclear masses without correcting the electron convention. Positive binding energy does not mean the bound system is heavier. Multiply binding per nucleon by the relevant nucleon count before comparing totals. After three half-lives, one eighth remains and seven eighths has decayed. Activity depends on both decay constant and parent count. A balanced A/Z equation is necessary bookkeeping, not proof of an energetically allowed channel.

Try it: decayed is not remaining

A single parent species has half-life 2 h. After 4 h, what fractions remain and have decayed in the ensemble model? Does the remaining fraction imply that every original nucleus had a fixed four-hour lifetime?

Try it: alpha then beta-minus

For a hypothetical parent with A=210 and Z=84, perform A/Z bookkeeping for one alpha emission followed by one beta-minus emission. What are the final A, Z and neutron count? Does bookkeeping alone establish that the chain is physically allowed?

Come back tomorrow: name the mass, count and energy basis

Write a binding-energy balance with one consistent mass convention. Then distinguish remaining population, decayed population and activity without looking at the graph. Revisit NEET Atoms to compare electronic and nuclear energy changes, or NEET Work, Energy and Power for initial/final energy bookkeeping.

Chapter practice opens the broad Nuclei pool.

Sources and review

Technical review: Codex (automated). Primary textbook sources checked on 23 October 2026. Diagrams, worked examples and self-checks are original. Numerical calculations use stated approximations and supplied rounded constants. Human subject review is not claimed. Chapter catalogues and these explanations do not establish complete coverage of every current examination format or syllabus.

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